All SAT Math Resources
Example Questions
Example Question #1 :How To Find An Angle In A Polygon
If angle A and angle C are complementary angles and B and D are supplementary angles, which of the following must be true?
A/D < B/C
None of the answers.
AD = BC
A * C > B * D
None of the answers.
This question is very misleading, because while each answer COULD be true, none of them MUST be true. Between angle A and C, onne of the angles could be very small (0.001 degrees) and the other one could be very large. For instance, if A = 89.9999 and C = 0.0001, AC = 0.009. On the other hand, the two angles could be very siimilar. If B = 90 and D = 90 then BD = 8100 and BD > AC. If we use these same values we disprove AD = BC as 8100 ≠ .009. Finally, if B is a very small value, then B/C will be very small and smaller than A/D.
Example Question #1 :How To Find An Angle In A Polygon
In isosceles triangleABC, the measure of angleAis 50 degrees. Which is NOT a possible measure for angleB?
There is more than one correct answer
95 degrees
65 degrees
80 degrees
50 degrees
95 degrees
If angleAis one of the base angles, then the other base angle must measure 50 degrees. Since 50 + 50 +x= 180 meansx= 80, the vertex angle must measure 80 degrees.
If angleAis the vertex angle, the two base angles must be equal. Since 50 +x+x= 180 meansx= 65, the two base angles must measure 65 degrees.
The only number given that is not possible is 95 degrees.
Example Question #1 :How To Find An Angle In A Polygon
In triangleABC, the measure of angleA= 70 degrees, the measure of angleB=xdegrees, and the measure of angleC=ydegrees. What is the value ofyin terms ofx?
110 –x
110 +x
70 –x
70 +x
x– 70
110 –x
Since the three angles of a triangle sum to 180, we know that 70 +x+y= 180. Subtract 70 from both sides and see thatx+y= 110. Subtractxfrom both sides and see thaty= 110 –x.
Example Question #1 :How To Find An Angle In A Polygon
What is the measure, in degrees, of each interior angle of a regular convex polygon that has twelve sides?
150
180
175
135
120
150
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n –2), wheren是双方的数量。问题涉及波尔ygon with twelve sides, so we will letn= 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150.
The answer is 150.
Example Question #102 :Plane Geometry
In the figure above, polygonABDFHGECis a regular octagon. What is the measure, in degrees, of angleFHI?
45
60
40
50
30
45
AngleFHIis the supplement of angleFHG, which is an interior angle in the octagon. When two angles are supplementary, their sum is equal to 180 degrees. If we can find the measure of each interior angle in the octagon, then we can find the supplement of angleFHG, which will give us the measure of angleFHI.
The sum of the interior angles in a regular polygon is given by the formula 180(n –2), wherenis the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This means that angleFHGhas a measure of 135 degrees.
Now that we know the measure of angleFHG, we can find the measure ofFHI. The sum of the measures ofFHGandFHImust be 180 degrees, because the two angles form a line and are supplementary. We can write the following equation:
Measure ofFHG+ measure ofFHI= 180
135 + measure ofFHI= 180
Subtract 135 from both sides.
Measure ofFHI= 45 degrees.
The answer is 45.
Example Question #101 :Plane Geometry
What is the measure of each angle in a regular octagon?
An octagon contains six triangles, or 1080 degrees. This means with 8 angles, each angle is 135 degrees.
Example Question #1 :Other Polygons
What is the measure of each central angle of an octagon?
There are 360 degrees and 8 angles, so dividing leaves 45 degrees per angle.
Example Question #11 :Other Polygons
What is the average (arithmetic mean) of all 15 interior angles of a quadrilateral, pentagon, and hexagon?
The 4 angles of a quadrilateral add to 360
The 5 angles of a pentagon add to 540
The 6 angles of a hexagon add to 720
Example Question #1 :How To Find An Angle In A Polygon
Find the sum of the interior angles in a nonagon.
To solve, simply use the formula for the total degrees in a polygon, where n is the number of vertices.
In this particular case, a nonagon is a shape with nine sides and thus nine vertices.
Thus,
Example Question #6 :How To Find An Angle In A Polygon
Which of the followingcannotbe the measure of an exterior angle of a regular polygon?
If one exterior angle is taken at each vertex of any convex polygon, the sum of their measures is. In a regular polygon - one with congruent sides and congruent interior angles, each exterior angle is congruent to one another. If the polygon hassides, each exterior angle has measure.
Given the common measure,
Multiplying both sides by:
and
Sinceis equal to a number of sides, it is a whole number. Thus, we are looking for a value ofwhich, when we divide 360 by it, yields a non-whole result. We see thatis the correct choice, since'
A quick check confirms that 360 divided by 8, 10, 12, or 15 yields a whole result.
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